Some subsets of the Hermitian curve

Donati, Giorgio; Durante, Nicola

doi:10.1016/s0195-6698(02)00143-9

Cited by 14 publications

(15 citation statements)

References 5 publications

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“…□ Remark 3.3. In [7] the authors define three kinds of subsets of PG(2, 2 ) of type (0, 1, 2, + 1) with respect to lines, where is any prime power. One of these sets, the − is constructed as follows.…”

Section: Lemma 31 Two Distinct Lines Of  Meet Either In a Vertex Omentioning

confidence: 99%

Blocking structures in finite projective planes

Aguglia

Cossidente

Pavese

2017

J of Combinatorial Designs

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Exploring the classical Ceva configuration in a Desarguesian projective plane, we construct two families of minimal blocking sets as well as a new family of blocking semiovals in PG(2, 32h). Also, we show that these blocking sets of PG(2, q2), regarded as pointsets of the derived André plane A(q2), are still minimal blocking sets in A(q2). Furthermore, we prove that the new family of blocking semiovals in PG(2, 32h) gives rise to a family of blocking semiovals in the André plane A(32h) as well.

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Section: Lemma 31 Two Distinct Lines Of  Meet Either In a Vertex Omentioning

confidence: 99%

Blocking structures in finite projective planes

Aguglia

Cossidente

Pavese

2017

J of Combinatorial Designs

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“…F set of PG(2, q 2 ) has been already studied in [3] (where it was called a C F -set) in the sequel, we may suppose that m < n/2.…”

Section: ( )mentioning

confidence: 99%

“…In [3] and [4], a (degenerate or not) C F -set in PG(2, q 2 ) is defined as the set of points of intersection of corresponding lines under a collineation with accompanying automorphism x → x q between two pencils of lines with vertices two distinct points A and B mapping the line AB onto itself or not. Every C F -set has q 2 + 1 points, and it is of type (0, 1, 2, q + 1) with respect to lines of PG(2, q 2 ), and every (q + 1)-secant line intersects a C F -set in a Baer subline (see [3]).…”

Section: Introductionmentioning

confidence: 99%

“…Every C F -set has q 2 + 1 points, and it is of type (0, 1, 2, q + 1) with respect to lines of PG(2, q 2 ), and every (q + 1)-secant line intersects a C F -set in a Baer subline (see [3]). Moreover, every C F -set is the union of A, and B with q − 1 Baer sublines and it is projectively equivalent to the set of GF(q 2 )-rational points of the algebraic curve with equation…”

Section: Introductionmentioning

confidence: 99%

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Scattered linear sets generated by collineations between pencils of lines

Donati

Durante

2014

J Algebr Comb

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Let A and B be two points of PG(2, q n ), and let be a collineation between the pencils of lines with vertices A and B. In this paper, we prove that the set of points of intersection of corresponding lines under is either the union of a scattered GF(q)-linear set of rank n + 1 with the line AB or the union of q − 1 scattered GF(q)-linear sets of rank n with A and B. We also determine the intersection configurations of two scattered GF(q)-linear sets of rank n + 1 of PG(2, q n ) both meeting the line AB in a GF(q)-linear set of pseudoregulus type with transversal points A and B.

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“…Let α F be the involutory automorphism of GF(q 2 ) and let Φ be an α F -collineation between P A and P B . If Φ does not map the line AB onto the line BA, then the set of points of intersections of corresponding lines under Φ is called a C F -set (see [4]). If Φ maps the line AB onto the line BA, then the set of points of intersections of corresponding lines under Φ is called a degenerate C F -set (see [5]).…”

Section: Introductionmentioning

confidence: 99%

Two projectively generated subsets of the Hermitian surface

Donati¹,

Durante²

2010

Innov. Incidence Geom.

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Using a variation of Seydewitz's method of projective generation of quadrics we define two algebraic surfaces of PG(3, q 2 ), called elliptic Q F -sets and semi-hyperbolic Q F -sets, and we show that these surfaces are contained in the Hermitian surface of PG(3, q 2 ). Also, we characterize a semi-hyperbolic Q F -set as the intersection of two Hermitian surfaces. Finally we describe all possible configurations of the absolute set of an α-correlation in PG(2, q 2 ), where α is the involutory automorphism of GF(q 2 ).

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Some subsets of the Hermitian curve

Cited by 14 publications

References 5 publications

Blocking structures in finite projective planes

Blocking structures in finite projective planes

Scattered linear sets generated by collineations between pencils of lines

Two projectively generated subsets of the Hermitian surface

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